Named for Monty Hall, host of “Let’s Make a Deal” game show, the situation is: You have a choice between the prize behind one of 3 doors, “Door number one, door number two, or door number three”, in his words. Behind one of these doors is a shiny new car. Behind the other two are goats. This is the “Monty Hall Dilemma”.

You have a 1 in 3 chance of picking the car. You pick a door, and Monty shows you what is behind one of the other two doors, which always has a goat. Now, he gives you the chance to change your choice of door. Do you change?

Monty of course knows which one is the winning door and intentionally showed you one of the doors that had a goat. One more has a goat, and the other has the shiny new car. Did you pick the car or the goat? And more importantly, should you change now?

  1. You originally had a 1 in 3 chance. Now there are two doors left, so you have a 1 in 2 chance. It doesn’t matter whether you stay with your choice.
  2. You originally had a 1 in 3 chance, and collectively the other doors had a 2 in 3 chance. Now your choice is between your original door and the “basket” of doors that had a 2 in 3 chance. You should change, and give yourself the 2 in 3 chance instead of the 1 in 3 that you started with.

Which explanation is the truth?

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Apparently pigeons are more experiential in their learning. When faced with the Monty Hall Dilemma they learn better than humans do. In Discover Ed Yong talks about pigeons ability to learn the correct answer better than humans. We have an ability to reason, but our reasoning doesn’t always get us to the right answer. We have a tendency toward sentimentality as well, which might keep us retaining our original choice. And it seems that the older we get, the harder it is for us to learn experientially like the pigeons do, as eighth graders apparently adapted better than college students. As we get older we rely more on our own reasoning and find it more difficult to get beyond or away from our conclusion.

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So here’s another version of the dilemma. Instead of just 3 choices, say you have 100 doors, and you choose one. Now, Monty opens 98 of the other unchosen doors to show you all the goats, leaving just one of the other doors closed. Now, are you going to keep your choice, or switch? Your door had a 1 in 100 chance of being the one with the car originally, as did all the other 99 doors. Now, what do you think your chances are of being the door with the car, or the chances of the last other closed door being the right one?

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The point of this, relative to poker, and besides the element of chance, is that we can be challenged when it comes to learning to adapt to reality. Apparently some people taking the test realized the 2/3 chance of the basket of doors and adapted their switching of their first choice to 2/3 times, as opposed to the pigeons who overall made a much better adjustment of always switching their choice, which is the best plan. Going to switching 2/3 of the time just gets you 2/3 of 2/3 chance plus 1/3 of the times you take the 1/3 chance, or 5/9 overall, as far as I can figure (correct me if I’m wrong; I’m limited in my reasoning ability too), as opposed to 2/3 or 6/9 chance that you have if you always take the 2/3 basket of doors.

Toss in selective memory and human opponents, and you can see why we have difficulty adapting to something with a multitude of outcomes, let alone a choice between 3 doors.

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